The \(U>0\)  Hubbard model is sign problem free if the system is particle-hole symmetric [1]}. This is the case at half filling (\(n=1\) ) on a bipartite lattice (e.g., square or honeycomb), when the intra-sublattice hopping is set to zero. Note that the sign of \(U\)  can be changed by performing a particle-hole transformation on one spin species, showing that the \(U<0\)  Hubbard model is sign problem free with zero total magnetization and an arbitrary filling. The Hubbard model has been simulated using DQMC on a square lattice [1]}, showing a clear Mott gap and an antiferromagnetic (Néel) ground state for all \(U>0\) .
